This invention relates to a technique for on-line system identification primarily for use with active control systems. A review of systems for active control of sound is given in "Active Control of Sound" by P. A. Nelson and S. J. Elliott, Academic Press, London. Most of the control systems used for active control are adaptive systems, wherein the controller characteristics or output is adjusted in response to measurements of the residual disturbance. If these adjustments are to improve the performance of the system, then knowledge is required of how the system will respond to any changes. This invention relates to methods for obtaining that knowledge.
Usually the system is characterized by the system impulse response, which is the time response at a particular controller input caused by an impulse at a particular output. The response therefore includes the response of the input and output processes of the system, such as actuator response, sensor response, smoothing and anti-aliasing filter responses etc. For multichannel systems, which have more than one input and/or output, a matrix of impulse responses is required, one for each input/output pair. For a sampled data representation the impulse response between the j-th output and the i-th input at the n-th sample will be denoted by a.sup.i j (n).
Equivalently, the system can be characterized by a matrix of transfer functions which correspond to the Fourier transforms of the impulse responses. These are defined, for the k-th frequency, by ##EQU1## where the k-th frequency is (k/NT) Hz and T is the sampling period in seconds.
The most common technique for system identification is to send a test signal from the controller output and measure the response at the controller input. In order to discriminate against other noise in the system, a random test signal is normally used, and this is correlated with the response. Other noises which are not correlated with the test signal are rejected.
In "Adaptive Signal Processing" by B. Widrow and S. D. Stearns, Prentice Hall, (1985), several adaptive schemes for system identification (or plant modeling) are described.
Provided that the test signal is uncorrelated with other system noise, the system identification can continue while an active control system is in operation. In U.S. Pat. No. 4,677,676 by L. J. Eriksson this is described for a single channel active control system in a duct. This system is typical of the prior art and is summarized in FIGS. 1 and 2. FIG. 1 shows the system identification system and control system in a duct or pipe. FIG. 2 shows the equivalent block diagram. These correspond to FIGS. 19 and 20 in the original document.
It is not recognized in Eriksson that the residual signal (44 in the Figures) used to adapt the control filters is contaminated by the test signal. This will cause the system to try to adapt to cancel the test signal--resulting in a random variation or `jitter` in the filter coefficients. This results in a reduced performance.
A further aspect of Eriksson and similar approaches is that on-line system identification is an adaptive filter and at each sampling interval every coefficient of the impulse response is updated. This is a computationally expensive operation and, since the signal processor has fixed processing power, this will slow down the maximum sampling rate of the controller and reduce its performance. Another aspect of Eriksson and similar approaches is that a random test signal (or noise source) is used.